Gate-Controlled Superconductivity in a Diffusive Multiwalled Carbon Nanotube

We have investigated electrical transport in a diffusive multiwalled carbon nanotube contacted using superconducting leads made of an $\mathrm{Al}/\mathrm{Ti}$ sandwich structure. We find proximity-induced superconductivity with measured critical currents up to $I_{\mathrm{cm}}=1.3\mathrm{nA}$, tunable by the gate voltage down to 10 pA. The supercurrent branch displays a finite zero bias resistance which varies as $R_0\propto I_{\mathrm{cm}}^{-\alpha }$ with $\alpha =0.74$. Using $IV$ characteristics of junctions with phase diffusion, a good agreement is obtained with the Josephson coupling energy in the long, diffusive junction model of A. D. Zaikin and G. F. Zharkov [Sov. J. Low Temp. Phys. 7, 184 (1981)].

Figure 1

Current $I$ as a function of bias voltage $V$ at gate voltage $V_g=3.214\mathrm{V}$ (●); 3.220 V (○); 3.232 V (▪); 3.232 V (□); 3.244 V (▴); 3.344 V (▵). The solid straight line displays the normal state $IV$ curve measured in a magnetic field of $B=0.2\mathrm{T}$ at $V_g=3.202\mathrm{V}$. The arrows A and B illustrate the determination of the maximum supercurrent $I_{\mathrm{cm}}$ in the nonhysteretic and hysteretic cases. The inset on the lower right illustrates a magnification of the $IV$ curve at $V_g=3.214\mathrm{V}$, where clear hysteresis is visible and the critical current $I_{\mathrm{cm}}=0.15\mathrm{nA}$. The inset on the upper left displays an AFM image of our sample (scale bar: $1\mu \mathrm{m}$). The data were measured in a two-lead configuration on the middle section at $T=65\mathrm{mK}$.

Figure 2

$I_{\mathrm{cm}}$ vs. zero bias resistance $R_0$ and normal state resistance $R_n$ measured at $T=80\mathrm{mK}$. The open and filled circles displays $R_0$ and $R_n$ at $V_g=3.21\dots 3.33\mathrm{V}$, respectively. The filled triangles denote $R_0$ at $V_g=5.98\dots 6.02\mathrm{V}$. The solid curve is a power law fit with $I_{\mathrm{cm}}\propto R_0^{-1.35}$ while the dashed line represents $I_{\mathrm{cm}}\propto R_n^{-4.93}$. The dotted curve displays the phase-diffusion relation $I_{\mathrm{cm}}\propto R_0^{-1}$ valid at $E_J\ll k_{B}T$. The inset displays the normal state conductance $G_n=1/R_n$ vs $V_g$. The range of the superconducting $IV$ curves in Fig. 1 ($V_g=3.214–3.244\mathrm{V}$) is indicated by the gray shading.

Figure 3

Temperature dependence of $I_{\mathrm{cm}}$ (●) and $R_0$ (○) measured at $V_g=3.489\mathrm{V}$. The solid curve is a fit obtained from Eqs. (2, 3) using $D=2.2\times {10}^{-3}{\mathrm{m}}^2/\mathrm{s}$, $L=0.4\mu \mathrm{m}$, and $R_n=17\mathrm{k}\Omega$. The dashed line displays $R_0$ calculated from Eq. (1) using $Z_{\mathrm{env}}=400\Omega$ and $E_J(T)$ from the above $T$-dependence fit.

Figure 4

Conductance $G$ vs bias voltage $V$. Gate voltage $V_g$ has been stepped over $V_g=3.323\dots 3.355\mathrm{V}$ in steps of 2 mV. The dashed vertical lines indicate locations for the first Andreev reflection process if governed by unrenormalized ${\Delta }_{\mathrm{lead}}/e=139\mu \mathrm{eV}$.